Understanding Orgone[7]

Orgone[7] is a 7 (unique) note per octave tuning. In 11-equal (11edo), it can be described as "Moment of symmetry" scale (MOS) where we are stacking every 3 steps of 11-edo ("using 3\11 as a generator") and taking the clock-arithmetic remainder (modulus) when we pass the octave (step #11 of 11-edo).

Recipe:

• Create a stack of 7 notes, 3\11 (or 3deg11 or "3 degrees of 11-edo") apart, wrapping like a clock around 11 (instead of 12):
  0 3 6 9 1 4 7 ("0" represents the starting pitch)
• Sort the list in order:
  0 1 3 4 6 7 9 (11) ("0" and "11" represent the same starting pitch)
• If we measure the "gaps" between the neighboring pitches in the series above, we get another way of representing the series:
  1 2 1 2 1 2 2

Notice it confirms to the definition of a MOS scale, it only has 2 sizes of gap, an 'L' and an 'S' (large and small, and we don't care what the relative size of 'L' and 'S' are, as long as there are only 2 sizes. Any scale with 2 step sizes is called a MOS, for "Moment of Symmetry". You can play around with a MOS JavaScript app here.

In cents, the scale would look like so:

0.0
109.090909091
327.272727273
436.363636364
654.545454545
763.636363636
981.818181818
1200.0

Just like any other scale, we can rotate the list of inter-note distances and get a different "mode", e.g. 1 2 1 2 2 1 2 instead of 1 2 1 2 1 2 2.